Certain weighted averages of generalized Ramanujan sums

DOI10.1007/s11139-016-9827-8zbMath1456.11007arXiv1601.06879OpenAlexW3102021886MaRDI QIDQ1694380

K. Vishnu Namboothiri

Publication date: 1 February 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06879

zbMATH Keywords

gamma functionBernoulli numbersJordan totient functionweighted averagegeneralized Ramanujan sum

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Gamma, beta and polygamma functions (33B15) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (7)

On the polynomial Ramanujan sums over finite fields ⋮ Sums of averages of generalized Ramanujan sums ⋮ On the mean square average of Dirichlet \(L\)-function over characters of odd parity in a special case ⋮ Covering sumsets of a prime field and class numbers ⋮ On the number of solutions of a restricted linear congruence ⋮ Sums of weighted averages of gcd-sum functions ⋮ The discrete Fourier transform of \((r, s)\)-even functions

Cites Work

• Ramanujan sums are nearly orthogonal to powers
• On the mean square average of special values of \(L\)-functions
• An extension of Ramanujan's sum. III: Connections with totient functions
• Generalized Ramanujan's sum
• Distribution of averages of Ramanujan sums
• Averages of Ramanujan sums: note on two papers by E. Alkan
• An extension of Ramanujan's sum
• A SURVEY OF RAMANUJAN EXPANSIONS
• RAMANUJAN SUMS AND THE BURGESS ZETA FUNCTION
• DEFINING POWER SUMS OF n AND φ(n) INTEGERS
• Averages of values of 𝐿-series
• Number Theory
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